Electronic – convert a toggle switch to momentary switch using a transistor and capacitor

You need to omit Rswitch so that the transistor base is pulled completely up to the emitter voltage....that's how you turn off a PNP transistor. 1k for Rbase will give you about 12mA of base current which seems like a reasonable choice. Without knowing anything about your LEDs it's hard to say whether the 150 ohm resistors have the right value. You might think about using two transistors, one for each string. You can just connect both bases to the switch and both emitters to 12V. That will reduce the power dissipated in the each transistor although it's probably not necessary.

If you are using a 5V supply - you must use 5V relay also, not 12V one.

Better not increase the capacity, but use a separate capacitor for each relay. You can still use just one main switch, make sure it's strong enough to withstand the sparks on discharging capacitors if you have many of them.

And you'll need a really powerful supply if you'll use many capacitors. And capacitor recharge times will affect the frequency of switchings you can achive.

You can add resistors to the capacitors and calculate the recharging time as per RC-circuit principle.